60.7.134 problem 1725 (book 6.134)

Internal problem ID [11723]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1725 (book 6.134)
Date solved : Tuesday, January 28, 2025 at 06:11:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.112 (sec). Leaf size: 21

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

\[ y = \frac {c_{2}^{2}-c_{2} x +c_{1}}{-x +c_{2}} \]

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 123

DSolve[2*D[y[x],x]*(1 + D[y[x],x]) + (x - y[x])*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=\frac {1}{2} \int \frac {(1-K[4]) \exp \left (-\int _1^{K[4]}\frac {1-K[3]}{2 K[3] (K[3]+1)}dK[3]-c_1\right )}{(K[4]-1) K[4] (K[4]+1)} \, dK[4]+c_2,y(x)=x-\exp \left (-\int _1^{K[4]}\frac {1-K[3]}{2 K[3] (K[3]+1)}dK[3]-c_1\right )\right \},\{y(x),K[4]\}\right ] \]