# Solving equations using Laplace transform

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Aleem Andrew
on 14 Jan 2021

Answered: Logeshwari S
on 19 Nov 2021

I am trying to solve an equation using the Laplace transform without having to find the Laplace transforms of the terms in the equation. Matlab is unable to find a solution based on the code below, although a solution can be found by writing the terms as a function of s. Could someone please suggest a method to do this?

syms y(t)

Dy2 = diff(y,t,2); Dy1 = diff(y,t,1);

eqn = laplace(Dy2+3*Dy1+2*y) == laplace(exp(-t))

cond = [y(0)==4, Dy(0)==5];

sol = dsolve(eqn,cond)

f

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### Accepted Answer

Star Strider
on 14 Jan 2021

Unless you are solving a partial differential equation, such that the Laplace transform produces an ordinary differential equation in one of the two variables and a Laplace transform of ‘t’, dsolve is not appropriate. It is simply necessary to solve for (in this instance) ‘Y(s)’ and then invert it to get ‘y(t)’:

syms t y(t) Y(s) Dy0

Dy2 = diff(y,t,2);

Dy1 = diff(y,t,1);

eqn = laplace(Dy2+3*Dy1+2*y == exp(-t))

eqn = subs(eqn, {laplace(y(t), t, s), subs(diff(y(t), t), t, 0)},{Y(s), Dy0})

cond = [y(0)==4, Dy1(0)==5];

Soln_s = isolate(eqn, Y(s))

Soln_t = ilaplace(Soln_s)

Soln_t = subs(Soln_t, {ilaplace(Y(s), s, t)}, {y(t)})

Soln_t = simplify(Soln_t, 'Steps',500)

.

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### More Answers (1)

Logeshwari S
on 19 Nov 2021

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