# Simplifying solution of a differential equation

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Aleem Andrew
on 14 Jan 2021

Commented: Aleem Andrew
on 14 Jan 2021

The most simplified version of ySol(t), the solution to the differential equation below, is 1.5*sin(2t+0.7297), but the output of the following code is in terms of exponential functions. Can someone explain how the output can be further simplified?

syms y(t) m k

Dy = diff(y,t); Dy2 = diff(y,t,2);

ode = m*Dy2 + k*y == 0;

cond = [y(0) == 1,Dy(0) == sqrt(5)];

ySol(t) = dsolve(ode,cond)

ySol(t) = simplify(ySol(t),'steps',500)

pretty(ySol(t))

##### 4 Comments

Walter Roberson
on 14 Jan 2021

### Accepted Answer

Walter Roberson
on 14 Jan 2021

m = rand(); k = rand();

syms y(t)

Dy = diff(y,t);

Dy2 = diff(y,t,2);

ode = m*Dy2 + k*y == 0;

cond = [y(0) == 1,Dy(0) == sqrt(5)];

ySol(t) = dsolve(ode,cond)

ySol(t) = simplify(ySol(t),'steps',500)

pretty(ySol(t))

vpa(ySol(t), 5)

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