Internal problem ID [10160]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y-x \right )^{2} y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 29
dsolve((y(x)-x)^2*diff(y(x),x)=1,y(x), singsol=all)
\[ y \relax (x )+\frac {\ln \left (y \relax (x )-x -1\right )}{2}-\frac {\ln \left (y \relax (x )-x +1\right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 33
DSolve[(y[x]-x)^2*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)+\frac {1}{2} \log (-y(x)+x+1)-\frac {1}{2} \log (y(x)-x+1)=c_1,y(x)\right ] \]