how to solve this differential equations with dsolve

how do i solve this equations with dsolve? And how must be the syntax into the inline code so i can plot them in the end?

2*y''+3x^2*y=exp(2*x) y(1)=3 , y'(2)=0

y''-3*x^2*y=1/x y(1)=3 , y'(2)=-1

Answer 1

[Ronit]

Hello,

To solve differential equations using ‘dsolve’ in MATLAB, you need to set up the equations and initial conditions properly. Here's how you can solve the given equations:

syms y(x) 
Dy = diff(y, x); 
D2y = diff(y, x, 2); 

% First differential equation 
eq1 = 2*D2y + 3*x^2*y == exp(2*x); 
cond1 = [y(1) == 3, subs(Dy, x, 2) == 0]; 
sol1 = dsolve(eq1, cond1); 

% Second differential equation 
eq2 = D2y - 3*x^2*y == 1/x; 
cond2 = [y(1) == 3, subs(Dy, x, 2) == -1]; 
sol2 = dsolve(eq2, cond2); 

This kind of equations involves an integral that is difficult to evaluate numerically. So, the solution contains complex expressions or when the integrals do not converge easily. I suggest you try a different approach by using numerical solvers like ‘ode45’ to solve the differential equations instead of relying on ‘dsolve’. This approach involves converting the problem to initial value problems and using numerical methods to solve them. And you can use ‘deval’ function in MATLAB to evaluate the solution ‘ode45’ solver.

Please find the following documentation links for more information:

1. ode45: https://www.mathworks.com/help/matlab/ref/ode45.html
2. deval: https://www.mathworks.com/help/matlab/ref/deval.html
3. dsolve: https://www.mathworks.com/help/symbolic/dsolve.html

Hope it helps!