Internal problem ID [2686]
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]
\[ \boxed {y^{\prime }-\frac {y}{x}-\frac {4 x^{2} \cos \left (x \right )}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = \sqrt {8 \sin \left (x \right )+c_{1}}\, x y \left (x \right ) = -\sqrt {8 \sin \left (x \right )+c_{1}}\, x \end{align*}
✓ Solution by Mathematica
Time used: 0.298 (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*}