Internal problem ID [12140]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {n y}{x}={\mathrm e}^{x} x^{n}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x)-n/x*y(x)=exp(x)*x^n,y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{x}+c_{1} \right ) x^{n} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 15
DSolve[y'[x]-n/x*y[x]==Exp[x]*x^n,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (e^x+c_1\right ) x^n \]