29.28.1 problem 798

Internal problem ID [5382]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 798
Date solved : Monday, January 27, 2025 at 11:17:35 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 53

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 59

DSolve[(D[y[x],x])^2+a* x *D[y[x],x]==b*c*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} x^2 \left (\sqrt {a^2+4 b c}-a\right )+c_1 \\ y(x)\to -\frac {1}{4} x^2 \left (\sqrt {a^2+4 b c}+a\right )+c_1 \\ \end{align*}