29.19.32 problem 545

Internal problem ID [5141]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 545
Date solved : Monday, January 27, 2025 at 10:14:12 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 45

dsolve(2*x*y(x)*diff(y(x),x)+x^2*(a*x^3+1) = 6*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {4 c_{1} x^{4}+4 a \,x^{3}+1}\, x}{2} \\ y \left (x \right ) &= \frac {\sqrt {4 c_{1} x^{4}+4 a \,x^{3}+1}\, x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.949 (sec). Leaf size: 59

DSolve[2 x y[x] D[y[x],x]+x^2(1+a x^3)==6 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2} \\ y(x)\to \frac {1}{2} \sqrt {4 a x^5+4 c_1 x^6+x^2} \\ \end{align*}