60.1.232 problem 233

Internal problem ID [10246]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 233
Date solved : Monday, January 27, 2025 at 06:41:30 PM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 30

dsolve(x*y(x)*diff(y(x),x)-y(x)^2+a*x^3*cos(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.324 (sec). Leaf size: 58

DSolve[x*y[x]*D[y[x],x]-y[x]^2+a*x^3*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {2 \int _1^x-a \cos (K[1])dK[1]+c_1} \\ y(x)\to x \sqrt {2 \int _1^x-a \cos (K[1])dK[1]+c_1} \\ \end{align*}