74.7.35 problem 35

Internal problem ID [16112]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:41:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 t y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 16

dsolve([diff(y(t),t)=(4*y(t)^2-t^2)/(2*t*y(t)),y(1) = 1],y(t), singsol=all)
 

\[ y = \frac {\sqrt {2 t^{2}+2}\, t}{2} \]

✓ Solution by Mathematica

Time used: 0.578 (sec). Leaf size: 22

DSolve[{D[y[t],t]==(4*y[t]^2-t^2)/(2*t*y[t]),{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sqrt {t^4+t^2}}{\sqrt {2}} \]