29.28.4 problem 801

Internal problem ID [5385]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 801
Date solved : Monday, January 27, 2025 at 11:17:40 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 50

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 51

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

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