29.19.28 problem 541

Internal problem ID [5137]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 541
Date solved : Monday, January 27, 2025 at 10:13:53 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }&=a x +y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 44

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

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