Question

the differencial equation of family lines having intercept 'a'and 'b' on the both the axis respectively is ( 1. ay"+b=0 ,2. y'=0 ,3. ay'+b=0 ,4.y"=0​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The differential equation of family lines having intercept 'a' and 'b' on the both the axis respectively

1. ay" + b = 0

2. y' = 0

3. ay' + b = 0

4. y" = 0

EVALUATION

Here the equation of the line having intercept as a and b on the x axis and y axis respectively is given by

$\displaystyle \sf{ \frac{x}{a} + \frac{y}{b} = 1}$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{1}{a} + \frac{y'}{b} = 0}$

$\displaystyle \sf{ \implies \: \frac{y'}{b} = - \frac{1}{a} }$

Again Differentiating both sides with respect to x we get

$\displaystyle \sf{ \implies \: \frac{y''}{b} =0}$

$\displaystyle \sf{ \implies \: y''=0}$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{4. \: \: \: \: y''=0}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Solve the differential equation :-

(cosx.cosy - cotx) dx - (sinx.siny) dy=0

https://brainly.in/question/23945760

2. For the differential equation $xy \frac{dy}{dx}=(x+2)(y+2)$ , find the solution curve passing through the poin...

https://brainly.in/question/8138112