If y- Pe ax - Qe bx- show thatd 2 y - dx 2- a - b dy - dx - aby -0 -

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Implicit Differentiation

If y= Pe ax +...

Question

If y=Pe^ax+Qe^bx , show that
d²y/dx²-(a+b)dy/dx+aby=0.

Open in App

Solution

Suggest Corrections

Similar questions

If $y = P e^{a x} + Q e^{b x}$ , then prove that $\frac{d^{2} y}{d x^{2}} - (a + b) \frac{d y}{d x} + a b y = 0$

y = P e^{a x} + Q e^{h x}

\frac{d^{2} y}{d x^{2}} - (a + b) \frac{d y}{d x} + a b y = 0

y = e^{a x} cos b x

\frac{d^{2} y}{d x^{2}} - 2 a \frac{d y}{d x} + (a^{2} + b^{2}) y = 0

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} e^{- x}

\frac{d^{3} y}{{d x}^{3}} + a \frac{d^{2} y}{d x^{2}} + b \frac{d y}{d x} + c y = 0

\frac{a^{3} + b^{3} + c^{3}}{a b c}

y = 3 cos (log x) + 4 sin (log x)

x^{2} \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + y = 0

Join BYJU'S Learning Program