76.5.7 problem 7

Internal problem ID [17427]
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 : 7
Date solved : Tuesday, January 28, 2025 at 10:08:10 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 y-7 x}{5 x -y} \end{align*}

✓ Solution by Maple

Time used: 1.812 (sec). Leaf size: 53

dsolve(diff(y(x),x)=(4*y(x)-7*x)/(5*x-y(x)),y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {-7 x^{2}-x y+y^{2}}{x^{2}}\right )}{2}+\frac {9 \sqrt {29}\, \operatorname {arctanh}\left (\frac {\left (x -2 y\right ) \sqrt {29}}{29 x}\right )}{29}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 40

DSolve[D[y[x],x]==(4*y[x]-7*x)/(5*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-5}{K[1]^2-K[1]-7}dK[1]=-\log (x)+c_1,y(x)\right ] \]