29.27.31 problem 797

Internal problem ID [5381]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 797
Date solved : Monday, January 27, 2025 at 11:17:34 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}-4 \left (1+x \right ) y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2-4*(1+x)*diff(y(x),x)+4*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 27

DSolve[(D[y[x],x])^2-4*(1+x)*D[y[x],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*}