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 = 0.0101323 (sec), leaf count = 14

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

Maple
cpu = 0.005 (sec), leaf count = 12

\[ \left \{ y \relax (x ) =x \left (-\cos \relax (x ) +{\it \_C1} \right ) \right \} \] 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),'implicit')

Maple raw output

y(x) = x*(-cos(x)+_C1)