29.19.31 problem 544

Internal problem ID [5140]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 544
Date solved : Monday, January 27, 2025 at 10:14:07 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }&=4 x^{2} \left (1+2 x \right )+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(2*x*y(x)*diff(y(x),x) = 4*x^2*(1+2*x)+y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {\left (4 x^{2}+c_{1} +4 x \right ) x} \\ y \left (x \right ) &= -\sqrt {\left (4 x^{2}+c_{1} +4 x \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 52

DSolve[2 x y[x] D[y[x],x]==4 x^2(1+2 x)+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x} \sqrt {4 x^2+4 x+c_1} \\ y(x)\to \sqrt {x} \sqrt {4 x^2+4 x+c_1} \\ \end{align*}