Internal problem ID [74]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -x^{4} \cos \relax (x )-3 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (2 \pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 10
dsolve([x*diff(y(x),x) = x^4*cos(x)+3*y(x),y(2*Pi) = 0],y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 11
DSolve[{x*y'[x] == x^4*Cos[x]+3*y[x],y[2*Pi]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 \sin (x) \\ \end{align*}