Internal problem ID [2313]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve([(1-exp(x))*diff(y(x),x$2)=exp(x)*diff(y(x),x),y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\left (\ln \left ({\mathrm e}^{x}\right )+\ln \left (-1+{\mathrm e}\right )-\ln \left (-1+{\mathrm e}^{x}\right )-1\right ) \left (-1+{\mathrm e}\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 27
DSolve[{(1-Exp[x])*y''[x]==Exp[x]*y'[x],{y[1]==0,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 (e-1) \left (\text {arctanh}(1-2 e)-\text {arctanh}\left (1-2 e^x\right )\right ) \]