77.1.16 problem 30 (page 38)

Internal problem ID [17906]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 30 (page 38)
Date solved : Tuesday, January 28, 2025 at 11:12:01 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }-4 y&=x^{2} \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(x*diff(y(x),x)-4*y(x)=x^2*sqrt(y(x)),y(x), singsol=all)
 

\[ \sqrt {y}-c_{1} x^{2}-\frac {\ln \left (x \right ) x^{2}}{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 21

DSolve[x*D[y[x],x]-4*y[x]==x^2*Sqrt[ y[x] ],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} x^4 (\log (x)+2 c_1){}^2 \]