Internal problem ID [2309]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2} \sin \left (x \right )=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✗ Solution by Maple
dsolve([diff(y(x),x$2)=diff(y(x),x)^2*sin(x),y(0) = 0, D(y)(0) = 1/2],y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 1.773 (sec). Leaf size: 6
DSolve[{y''[x]==y'[x]^2*Sin[x],{y[0]==0,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {Indeterminate} \]