Internal problem ID [10182]
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 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve((1+exp(y(x)/x))+exp(x/y(x))*(1-x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{\frac {1}{\textit {\_a}}} \left (\textit {\_a} -1\right )}{\textit {\_a} \left (\textit {\_a} \,{\mathrm e}^{\frac {1}{\textit {\_a}}}+{\mathrm e}^{\textit {\_a}}-{\mathrm e}^{\frac {1}{\textit {\_a}}}+1\right )}d \textit {\_a} +\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.484 (sec). Leaf size: 54
DSolve[(1+Exp[y[x]/x])+Exp(x/y[x])*(1-x/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-1}{K[1] \left (K[1] \text {Exp}-\text {Exp}+e^{K[1]} K[1]+K[1]\right )}dK[1]=-\frac {\log (x)}{\text {Exp}}+c_1,y(x)\right ] \]