4.4.2 \(x y'(x)=x^2 \sin (x)+y(x)\)

ODE
\[ x y'(x)=x^2 \sin (x)+y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.167091 (sec), leaf count = 14

\[\{\{y(x)\to x (-\cos (x)+c_1)\}\}\]

Maple
cpu = 0.006 (sec), leaf count = 12

\[[y \left (x \right ) = \left (-\cos \left (x \right )+\textit {\_C1} \right ) x]\] Mathematica raw input

DSolve[x*y'[x] == x^2*Sin[x] + y[x],y[x],x]

Mathematica raw output

{{y[x] -> x*(C[1] - Cos[x])}}

Maple raw input

dsolve(x*diff(y(x),x) = x^2*sin(x)+y(x), y(x))

Maple raw output

[y(x) = (-cos(x)+_C1)*x]