75.12.34 problem 308

Internal problem ID [16900]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 308
Date solved : Tuesday, January 28, 2025 at 09:40:15 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \end{align*}

✓ Solution by Maple

Time used: 26.544 (sec). Leaf size: 92

dsolve((5*x-7*y(x)+1)*diff(y(x),x)+(x+y(x)-1)=0,y(x), singsol=all)
 

\[ y = \frac {-\operatorname {RootOf}\left (7 \textit {\_Z}^{16}+\left (-128 c_{1} x^{4}+256 c_{1} x^{3}-192 c_{1} x^{2}+64 c_{1} x -8 c_{1} \right ) \textit {\_Z}^{4}-16 c_{1} x^{4}+32 c_{1} x^{3}-24 c_{1} x^{2}+8 c_{1} x -c_{1} \right )^{12}+16 x c_{1} \left (-\frac {1}{2}+x \right )^{3}}{2 c_{1} \left (-1+2 x \right )^{3}} \]

✓ Solution by Mathematica

Time used: 60.319 (sec). Leaf size: 8165

DSolve[(5*x-7*y[x]+1)*D[y[x],x]+(x+y[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

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