If = ^ -1 show that (1+x^2)y_2+(2x-1)y_1=0 - Vidyadip

Question

If $\log\text{y}=\tan^{-1}$ show that $(1+\text{x}^2)\text{y}_2+(2\text{x}-1)\text{y}_1=0$

✓

Answer

Here$\log\text{y}=\tan^{-1}$
Differentiating w.r.t.x, we get
$\frac{1}{\text{y}}\times\text{y}_1=\frac{1}{1+\text{x}^2}$ $\Rightarrow(1+\text{x}^2)\text{y}_1=\text{y}$ $\Rightarrow(1+\text{x}^2)\text{y}_2+2\text{xy}_1=\text{y}_1$ $\Rightarrow(1+\text{x}^2)\text{y}_2+2\text{xy}_1-\text{y}_1=0$$\Rightarrow(1+\text{x}^2)\text{y}_2+(25\text{x}-1)\text{y}_1=0$
hence proved

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Higher Order Derivatives→Higher Order Derivatives — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the following differential equation
$5\frac{\text{dy}}{\text{dx}}=\text{e}^\text{x}\text{y}^4$

If the points (3, -2), (x, 2), (8, 8) are collinear, find x using determinant.

Diffrentiate the following w.r.t.x

$\cot \left(\frac{\log x}{2}\right)-\log \left(\frac{\cot x}{2}\right)$

Evaluate the following :

$\int \frac{1}{5-4 x-3 x^2} \cdot d x$

Evaluate the following integrals:
$\int\frac{1}{\sqrt{\text{x}}}\Big(1+\frac{1}{\text{x}}\Big)\text{dx}$

Differentiate $\log(1+\text{x}^2)$ with respect to $\tan^{-1}\text{x}$

Find $\frac{d y}{d x}$ if $y=\tan ^{-1}\left(\frac{5 x+1}{3-x-6 x^2}\right)$

Prove by vector method, that the angle subtended on semicircle is a right angle.

Find the identity element in the set of all rational numbers except -1 with respect to * defined by a * b = a+ b + ab.

If $\vec{\text{a}}=4\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{k}},$ then find $\big|2\hat{\text{b}}\times\vec{\text{a}}\big|.$