how to solve this equastion : y''-1=exp(x) second order diff. equastion by use matlab command please reply

how to solve this equastion : y''-1=exp(x) second order diff. equastion please reply

[Torsten]

y'' = 1 + exp(x)
-> y' = x + exp(x) + a1
-> y = 1/2*x^2 + exp(x) + a1*x + a2

a1, a2 are arbitrary constants to be deduced from the initial/boundary conditions.

Best wishes

Torsten.

Answer 1

[Dimitris Kalogiros]

Of course , Trosten gave the solution for this ODE, but maybe it worths to have a look on how we can use symbolic maths toolbox to handle these equations:

clear; clc;

syms x y(x) 
syms a_0 a_1

Dy=diff(y,x) %definition of first derivative

ode=diff(y,x,2)-1==exp(x) % definition of 2nd order ODE

cond1=y(0)==a_0   % initial conditions
cond2=Dy(0)==a_1

ySol(x)=dsolve(ode, [cond1 cond2]) %solve ODE

And if someone run this script, will receive :