Internal problem ID [5838]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS.
K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page
114
Problem number: Example 3.5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-1+y+x}{x -y+3}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 32
dsolve(diff(y(x),x)=(x+y(x)-1)/(x-y(x)+3),y(x), singsol=all)
\[ y \left (x \right ) = 2+\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x +1\right )+2 c_{1} \right )\right ) \left (-x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 59
DSolve[y'[x]==(x+y[x]-1)/(x-y[x]+3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (1-\frac {2 (x+1)}{-y(x)+x+3}\right )+\log \left (\frac {x^2+y(x)^2-4 y(x)+2 x+5}{2 (x+1)^2}\right )+2 \log (x+1)+c_1=0,y(x)\right ] \]