29.27.7 problem 773

Internal problem ID [5357]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 773
Date solved : Monday, January 27, 2025 at 11:17:14 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 84

DSolve[(D[y[x],x])^2-2*D[y[x],x]+a*(x-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

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