74.18.65 problem 73

Internal problem ID [16622]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 73
Date solved : Tuesday, January 28, 2025 at 09:13:00 AM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y^{\prime } y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 11

dsolve([t*(diff(y(t),t$2)*y(t)+diff(y(t),t)^2)+diff(y(t),t)*y(t)=1,y(1) = 1, D(y)(1) = 1],y(t), singsol=all)
 

\[ y = \sqrt {2 t -1} \]

✓ Solution by Mathematica

Time used: 0.371 (sec). Leaf size: 14

DSolve[{t*(D[y[t],{t,2}]*y[t]+D[y[t],t]^2)+D[y[t],t]*y[t]==1,{y[1]==1,Derivative[1][y][1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {2 t-1} \]