20.4.22 problem Problem 38

Internal problem ID [3657]
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
Date solved : Monday, January 27, 2025 at 07:52:25 AM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \end{align*}

✓ Solution by Maple

Time used: 0.012 (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: 0.289 (sec). Leaf size: 36

DSolve[D[y[x],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*}