60.1.329 problem 330

Internal problem ID [10343]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 330
Date solved : Monday, January 27, 2025 at 07:17:28 PM
CAS classification : [[_homogeneous, `class C`], _exact, _dAlembert]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 22

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

\[ y = -x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\left (1+f \left (\textit {\_a} \right )\right )d \textit {\_a} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 52

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

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