4.22 problem Problem 38

Internal problem ID [2177]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number: Problem 38.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _Bernoulli]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\frac {4 x^{2} \cos \relax (x )}{y}=0} \end {gather*}

Solution by Maple

Time used: 0.011 (sec). Leaf size: 28

dsolve(diff(y(x),x)-1/x*y(x)=4*x^2/y(x)*cos(x),y(x), singsol=all)
 

\begin{align*} y \relax (x ) = \sqrt {8 \sin \relax (x )+c_{1}}\, x \\ y \relax (x ) = -\sqrt {8 \sin \relax (x )+c_{1}}\, x \\ \end{align*}

Solution by Mathematica

Time used: 0.266 (sec). Leaf size: 36

DSolve[y'[x]-1/x*y[x]==4*x^2/y[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {8 \sin (x)+c_1} \\ y(x)\to x \sqrt {8 \sin (x)+c_1} \\ \end{align*}