60.7.133 problem 1724 (book 6.133)

Internal problem ID [11722]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1724 (book 6.133)
Date solved : Monday, January 27, 2025 at 11:31:47 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.139 (sec). Leaf size: 16

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

\[ y = \sqrt {c_{1} +2 x}\, c_{2} +c_{1} +x \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 99

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

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