MHT CET20249 May 2024Evening ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation d y ~d x = y+ x^2-y^2 x is
Options
- A⁻¹ y= x+ c , where c is a constant of integration.
- By x = ⁻¹ x+ c , where c is a constant of integration.'
- Cy x = x^2-y^2 + c , where c is a constant of integration.
- D⁻¹ ( y x )= x+ c , where c is a constant of integration.
Correct answer
D. ⁻¹ ( y x )= x+ c , where c is a constant of integration.
Step-by-step solution
aligned & d y ~d x = y+ x^2-y^2 x ...(i) & Put y= v x ...(ii) & ~d y ~d x = v +x ~d v ~d x ...(iii) aligned Substituting (ii) and (iii) in (i), we get array ll & v +x dv d x = v x+ x^2- v ^2 x^2 x & v +x ~d v ~d x = v + 1- v ^2 & x dv d x = 1- v ^2 & dv 1- v ^2 = d x x & ⁻¹( v )= |x|+ c & ⁻¹ ( y x )= |x|+ c array