29.18.31 problem 509

Internal problem ID [5105]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 509
Date solved : Monday, January 27, 2025 at 10:11:31 AM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} x y y^{\prime }&=a \,x^{3} \cos \left (x \right )+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 30

dsolve(x*y(x)*diff(y(x),x) = a*x^3*cos(x)+y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {2 a \sin \left (x \right )+c_{1}}\, x \\ y \left (x \right ) &= -\sqrt {2 a \sin \left (x \right )+c_{1}}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 38

DSolve[x y[x] D[y[x],x]==a x^3 Cos[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {2 a \sin (x)+c_1} \\ y(x)\to x \sqrt {2 a \sin (x)+c_1} \\ \end{align*}