76.5.35 problem 36

Internal problem ID [17455]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 10:38:55 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ y^{{3}/{4}}-1-{\mathrm e}^{-\frac {3 x}{4}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.211 (sec). Leaf size: 33

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

\begin{align*} y(x)\to \left (1+e^{-\frac {3}{4} (x-c_1)}\right ){}^{4/3} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}