The solution of d x d y = cy + d a x + b represents a parabola if

The given equation is with separable variables so ( cy + d ) d y = ( a x + b ) d x . Integrating we have 2 c y 2 + d y + K = 2 a x 2 + b x , K being the constant of integration. The last equation represents a parabola if c = 0 , a  = 0 or a = 0 , c  = 0 .

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableMedium2 minQB

MathematicsMediumsingle choice

The solution of $\frac{d y}{d x} = \frac{a x + b}{cy + d}$ represents a parabola if

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The given equation is with separable variables so $(cy + d) d y = (a x + b) d x$ . Integrating we have $\frac{c y ^{2}}{2} + d y + K = \frac{a x ^{2}}{2} + b x, K$ being the constant of integration. The last equation represents a parabola if $c = 0, a \neq = 0$ or $a = 0, c \neq = 0$ .

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: QB

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