I’m trying to solve the following very simple differential equation, but it seems Mathematica cannot give me an answer,

`FullSimplify[DSolve[{y''[x] == 2 A Sinh[B y[x]], y[0] == W, y[L] == W}, y[x], x]] `

Any thoughts? Thanks!

Skip to content
# Tag: DSolve

## Problems with Dsolve[] and simple function

## Why both DSolve and NDSolve are unable to solve a second-order differential equation?

## Solving Laplace PDE with DSolve

## How to make DSolve express constants in terms of the unknown function

## DSolve is not working

## Solve an Integral-differential equation with DSolve

## How to Solve $y'(x)=x\ln(y(x))$ with $y(1)=1$ using DSolve

## Plot the solution from DSolve

## Workaround for DSolve in V 12 when it gives undefined as solution to 1D heat PDE?

## DSolve Doesn’t Return a Solution or Error

100% Private Proxies – Fast, Anonymous, Quality, Unlimited USA Private Proxy!

Get your private proxies now!

I’m trying to solve the following very simple differential equation, but it seems Mathematica cannot give me an answer,

`FullSimplify[DSolve[{y''[x] == 2 A Sinh[B y[x]], y[0] == W, y[L] == W}, y[x], x]] `

Any thoughts? Thanks!

I am trying to solve a recurrence relation using generating functions method. After some long calculations, I have arrived to this second-order differential equation: $ 0.5 x^5 y”(x)+(2x^4+x^3)y'(x)+\left(x^3+x^2+x-1\right)y(x)+1=0$

and these conditions: $ y(0)=1, y'(0)=1$ . $ y(x)$ is the function that needs to be expanded as Taylor Series at $ x=0$ to obtain the sequence from the coefficients. However, when I try to solve it both using DSolve and NDSolve, I have no luck. With DSolve it just returns the request itself:

$ $ \text{DSolve}\left[\left\{0.5 x^5 y”(x)+(2. x+1) x^3 y'(x)+\left(1. x^3+x^2+x-1\right)y(x)+1=0,y(0)=1,y'(0)=1\right\},y,x\right]$ $

And with NDSolve I just receive errors and no equation:

`Power::infy: Infinite expression 1/0.^5 encountered. Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.`. `

$ \text{NDSolve}\left[\left\{0.5 x^5 y”(x)+(2. x+1) x^3 y'(x)+\left(1. x^3+x^2+x-1\right)y(x)+1=0,y(0)=1,y'(0)=1\right\},y,\{x,0,1\}\right]$

How could I resolve this problem?

I’m trying to get an analytical solution of Laplace PDE with Dirichlet boundary conditions (in polar coordinates). I managed to solve it numerically with NDSolveValue and I know there is an analytical solution and I know what it is, but I would like DSolve to return it. But DSolve returns the input.

`sol = DSolve[{Laplacian[ u[\[Rho], \[CurlyPhi]], {\[Rho], \[CurlyPhi]}, "Polar"] == 0, DirichletCondition[u[\[Rho], \[CurlyPhi]] == 0, 1 <= \[Rho] <= 2 && \[CurlyPhi] == 0], DirichletCondition[u[\[Rho], \[CurlyPhi]] == 0, 1 <= \[Rho] <= 2 && \[CurlyPhi] == \[Pi]], DirichletCondition[ u[\[Rho], \[CurlyPhi]] == Sin[\[CurlyPhi]], \[Rho] == 1 && 0 <= \[CurlyPhi] <= \[Pi]], DirichletCondition[ u[\[Rho], \[CurlyPhi]] == 0., \[Rho] == 2 && 0 <= \[CurlyPhi] <= \[Pi]]}, u, {\[Rho], 1, 2}, {\[CurlyPhi], 0, \[Pi]}]; `

If I do

`DSolve[y'[x] == y[x], y[x], x] `

Mathematica returns

`{{y[x] -> E^x C[1]}} `

Is there a way to have it return this instead?

`{{y[x] -> E^x y[0]}} `

I am trying to solve differential equation but, Mathematica is not giving any output. Any idea how to solve this or any alternate way to solve this differential equation. I appreciate your help.

`DSolve[{(54 g[r] + 3 r (13 Derivative[1][f][r] + 5 Derivative[1][g][r] + 4 r (f^\[Prime]\[Prime])[r]))/ r^2 == (48 g[r])/r + ( 40 (66 - 89 r + 28 r^2) Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3], 4, (9 r)/10])/( 40 Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3], 4, 9/10] + 3 Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, 9/10]) + 57 Derivative[1][f][r] + 13 Derivative[1][g][r] + 11 r (f^\[Prime]\[Prime])[r], (1/( r^4))(-132 g[r] + 114 r g[r] - (r^3 (40 (-89 + 56 r) Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3], 4, (9 r)/10] + 9 (66 - 89 r + 28 r^2) Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, (9 r)/10]))/(40 Hypergeometric2F1[ 2 - Sqrt[3], 2 + Sqrt[3], 4, 9/10] + 3 Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, 9/10]) - 15 r Derivative[1][f][r] + 11 r^2 Derivative[1][f][r] + 39 r Derivative[1][g][r] - 59 r^2 Derivative[1][g][r] + 15 r^2 (f^\[Prime]\[Prime])[r] - 13 r^3 (f^\[Prime]\[Prime])[r] + 27 r^2 (g^\[Prime]\[Prime])[r] - 24 r^3 (g^\[Prime]\[Prime])[r]) == 0}, {f[r], g[r]}, r] `

I do not understand why the following code does not solve the equation:

`ClearAll eqn = y[t] == \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]\(Exp[ a \((t - s)\)] y[s] \[DifferentialD]s\)\); sol = DSolve[eqn, y[t], t, y[0] = 1] `

Can someone help me please? Thanks in advance.

The solution to $ y’=x \ln(y)$ with initial conditions $ y(1)=1$ is $ y=1$ .

How to persuade `DSolve`

to obtain this solution?

`ClearAll[y, x]; ode = y'[x] == x Log[y[x]]; ic = y[1] == 1; sol = DSolve[{ode, ic}, y[x], x] `

One can see that $ y=1$ is solution that also satisfies the ic by looking at direction field.

`ClearAll[x, y]; fTerm = x Log[y]; StreamPlot[ {1, fTerm}, {x, -1, 3}, {y, 0, 2}, Axes -> True, Frame -> False, PlotTheme -> "Classic", AspectRatio -> 1 / GoldenRatio, StreamPoints -> {{{{1, 1}, Red}, Automatic}}, Epilog -> {{Red, PointSize[.025], Point[{1, 1}]}}, PlotLabel -> Style[Text[Row [{"Solution curve with initial conditions at {", 1, ",", 1,"}"}]], 14] ] `

V 12.0 on windows 10

I’m trying to solve a differential equation as in the following code:

`FullSimplify[DSolve[x'[t] == a + b E^(g t) + (c + d E^(-g t)) x[t], x[t], t]] `

which generates

Now, I would like to plot it with specific parameter values assigned, for example: `a = 1; b = 2; c = 3; d = 4; g = 0.1; A = 1`

where I replaced the integration constant `c_1`

with `A`

.

Here is my code for plotting `x[t]`

:

`a = 1; b = 2; c = 3; d = 4; g = 0.1; A = 1 x[t_] := E^(-((d E^(-g t))/g) + c t) (A + Integrate[E^((d E^(-g K[1]))/g - c K[1]) (a + b E^(g K[1])), {K[1], 1, t}]) Plot[x[t], {t, 1, 10}] `

It runs forever. To check whether Mathematica is doing calculations, I tried

`x[1] `

and it yielded

`3.83926*10^-15 `

which is nice. But when I tried

`x[2] `

I got

It seems Mathematica cannot compute the integral unless the integration region is $ \int_1^1$ . Is this because the integrand is too complicated? Is there any way to let Mathematica compute it? Thanks!

Comparing the following, all done from clean kernel

The strange thing is that V 12 can solve this same PDE without the assumptions

`k = 1/10; A = 60; pde = D[u[x, t], t] == k*D[u[x, t], {x, 2}]; bc = u[0, t] == A; ic = u[x, 0] == 0; sol = DSolve[{pde, bc, ic}, u[x, t], {x, t}] `

But it says in the above answer that it wants `x>0,t>0`

, which is why I gave it the assumptions to help it, but then it returns undefined.

Something seems to have gone wrong in V 12 `DSolve`

here, or may be in the `Integrate`

? I do not know.

Do others see the same result on V 12?. Answer given by V 11.3 is the correct one.

Any workaround for V 12 to make it give same answer as V 11.3?

DSolve is not returning anything other than the original expression on

`DSolve[{z''[s] + 2/(R^2 - z[s]^2 - y[s]^2) (z[s]*z'[s]^2 + 2*y[s]*y'[s] z'[s] - z[s] y'[s]^2) == 0, y''[s] + 2/(R^2 - z[s]^2 - y[s]^2)*(y[s]*y'[s]^2 + 2*z[s]*z'[s]*y'[s] - y[s]*z'[s]^2) == 0}, {z[s], y[s]}, s] `

Am I doing something wrong or is this differential equation too difficult?

DreamProxies - Cheapest USA Elite Private Proxies
100 Private Proxies
200 Private Proxies
400 Private Proxies
1000 Private Proxies
2000 Private Proxies
ExtraProxies.com - Buy Cheap Private Proxies
Buy 50 Private Proxies
Buy 100 Private Proxies
Buy 200 Private Proxies
Buy 500 Private Proxies
Buy 1000 Private Proxies
Buy 2000 Private Proxies
ProxiesLive
Proxies-free.com
New Proxy Lists Every Day
Proxies123