Internal problem ID [7910]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 330.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _dAlembert]
Solve \begin {gather*} \boxed {\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 22
dsolve((f(x+y(x))+1)*diff(y(x),x)+f(x+y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = -x +\RootOf \left (-x +\int _{}^{\textit {\_Z}}\left (1+f \left (\textit {\_a} \right )\right )d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 52
DSolve[f[x + y[x]] + (1 + f[x + y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (f(x+K[2])-\int _1^xf'(K[1]+K[2])dK[1]+1\right )dK[2]+\int _1^xf(K[1]+y(x))dK[1]=c_1,y(x)\right ] \]