7.5.50 problem 50

Internal problem ID [154]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 50
Date solved : Friday, February 07, 2025 at 07:58:53 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)=(x+diff(y(x),x))^2,y(x), singsol=all)
 

\[ y = -\frac {x^{2}}{2}-\ln \left (-\cos \left (x \right ) c_1 +c_2 \sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 6.151 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]==(x+D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2}{2}-\log (\cos (x+c_1))+c_2 \]