Internal problem ID [1988]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y x={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)-x*y(x)=exp(x^2/2)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\sin \left (x \right )+c_{1} \right ) {\mathrm e}^{\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 20
DSolve[y'[x]-x*y[x]==Exp[x^2/2]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {x^2}{2}} (\sin (x)+c_1) \]