15.18.37 problem 37

Internal problem ID [3280]
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
Date solved : Monday, January 27, 2025 at 07:30:44 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&={\frac {1}{2}} \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: 1.878 (sec). Leaf size: 6

DSolve[{D[y[x],{x,2}]==D[y[x],x]^2*Sin[x],{y[0]==0,Derivative[1][y][0] ==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {Indeterminate} \]