28.4 problem 801

Internal problem ID [3533]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 28
Problem number: 801.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\left (b x +a \right ) y^{\prime }+c -b y=0} \end {gather*}

Solution by Maple

Time used: 0.098 (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 \relax (x ) = \frac {-b^{2} x^{2}-2 b x a -a^{2}+4 c}{4 b} \\ y \relax (x ) = c_{1} x +\frac {c_{1} a +c_{1}^{2}+c}{b} \\ \end{align*}

Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 43

DSolve[(y'[x])^2+(a+b x)y'[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+b x)^2-4 c}{4 b} \\ \end{align*}