74.4.33 problem 33

Internal problem ID [15926]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 08:22:57 AM
CAS classification : [_separable]

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(4*(x-1)^2*diff(y(x),x)-3*(y(x)+3)^2=0,y(x), singsol=all)
 

\[ y = \frac {\left (9-9 x \right ) c_{1} -4 x +13}{-3+\left (3 x -3\right ) c_{1}} \]

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 37

DSolve[4*(x-1)^2*D[y[x],x]-3*(y[x]+3)^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-4 (1+3 c_1) x+13+12 c_1}{-3+4 c_1 (x-1)} \\ y(x)\to -3 \\ \end{align*}