Internal problem ID [3529]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 797.
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}-4 \left (x +1\right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 25
dsolve(diff(y(x),x)^2-4*(1+x)*diff(y(x),x)+4*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x^{2}+2 x +1 \\ y \relax (x ) = c_{1} x -\frac {1}{4} c_{1}^{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 27
DSolve[(y'[x])^2-4(1+x)y'[x]+4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} c_1 (-4 x-4+c_1) \\ y(x)\to (x+1)^2 \\ \end{align*}