4.12 problem 12

Internal problem ID [12648]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 12.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]

\[ \boxed {y^{\prime }+\frac {y}{x}-y^{\frac {1}{4}}=0} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

\[ y \left (x \right )^{\frac {3}{4}}-\frac {3 x}{7}-\frac {c_{1}}{x^{\frac {3}{4}}} = 0 \]

✓ Solution by Mathematica

Time used: 9.843 (sec). Leaf size: 31

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

\[ y(x)\to \frac {\left (3 x+\frac {7 c_1}{x^{3/4}}\right ){}^{4/3}}{7 \sqrt [3]{7}} \]