74.7.25 problem 25

Internal problem ID [16102]
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 : 25
Date solved : Tuesday, January 28, 2025 at 08:40:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 2.039 (sec). Leaf size: 52

dsolve((2*t^2-7*t*y(t)+5*y(t)^2)+(t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \frac {t \left (-2 c_{1} t^{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-3 c_{1} t^{2}+2 \textit {\_Z} \right )\right )}{-3 c_{1} t^{2}+2 \operatorname {RootOf}\left (\textit {\_Z}^{4}-3 c_{1} t^{2}+2 \textit {\_Z} \right )} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 42

DSolve[(2*t^2-7*t*y[t]+5*y[t]^2)+(t*y[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]}{(2 K[1]-1) (3 K[1]-2)}dK[1]=-\log (t)+c_1,y(t)\right ] \]