Solution of nonlinear ordinary differential equation of second order

Can anyone let me hownto solve nonlinear ordinary differential equation mathematically, numerically and graphically using matlab. The differential equation is: y" = A (x^4) and y(0) = y(1) = 1

[Dyuman Joshi]

Do you mind showing how to solve a Differential equation graphically?

Also, did you search on this forum or on the internet for similar questions asked before?

Answer 1

[Torsten]

I suggest you integrate the equation

y" = A (x^4)

twice with respect to x and adjust the two free constants from the integration such that the two boundary conditions

y(0) = y(1) = 1

are satisfied.

No MATLAB is required.

Answer 2

[Bhumi Desai]

A = 1; % Assumed

syms y(x)

Dy = diff(y);

ode = diff(y,x, 2) == A*(x^4);

cond1 = y(0) == 1;

cond2 = y(1) == 1;

conds = [cond1 cond2];

ySol(x) = dsolve(ode,conds);

ySol = simplify(ySol)