If y=e^ 2x (ax+b), show that y_2-4y_1+4y=0 - Vidyadip

Question

If $\text{y}=\text{e}^{2\text{x}}(\text{ax}+\text{b}),$ show that $\text{y}_2-\text{4}\text{y}_1+4\text{y}=0$

✓

Answer

$\text{y}=\text{e}^{2\text{x}}(\text{ax}+\text{b}),$ Differentiating w.r.t.x, $\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{e}^{2\text{x}}(\text{a})+2(\text{ax}+b)(\text{e}^{2\text{x}})$ $\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{ae}^{2\text{x}}+2\text{y} $ Differentiating w.r.t.x,$\Rightarrow\frac{\text{dy}}{\text{dx}}=2\text{ae}^{2\text{x}}+2\frac{\text{dy}}{\text{dx}}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\frac{\text{dy}}{\text{dx}}+2\text{ae}^{2\text{x}}+4\text{y}-4\text{y}=2\frac{\text{dy}}{\text{dx}}+2\frac{\text{dy}}{\text{dx}}-4\text{y}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}-4\frac{\text{dy}}{\text{dx}}+4\text{y}=0$
$\Rightarrow\text{y}_2-4\text{y}_1+4\text{y}=0$
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.(5 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

Using differentials, find the approximate values of the following:
$(0.007)^{\frac{1}{3}}$

Let $Z$ be the set of all integers and $Z_0$ be the set of all non-zero integers. Let a relation $R$ on $Z \times Z_0$ be defined as $(a, b)R(c, d) ⇔ ad = bc$ for all $(a, b), (c, d) \in Z \times Z_0,$ Prove that $R$ is an equivalence relation on $Z \times Z_0.$

There are three urns $A, B,$ and $C$. Urn $A$ contains $4$ red balls and $3$ black balls. urn $B$ contains $5$ red balls and $4$ black balls. Urn $C$ contains $4$ red and $4$ black balls. One ball is drawn from each of these urns. What is the probability that $3$ balls drawn consists of $2$ red balls and a black ball?

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = x^4 - 4x^3 - 4x^2 + 15$

Find the equation of the plane determined by the intersection of the lines $\frac{\text{x}+3}{3}=\frac{\text{y}}{-2}=\frac{\text{z}-7}{6}$ and $\frac{\text{x}+6}{1}=\frac{\text{y}+5}{-3}=\frac{\text{z}-1}{2}$

Differentiate the following functions with respect to x:
$\text{e}^{\text{x}\log\text{x}}$

Evaluate:
$\begin{vmatrix}1&\text{a}&\text{bc}\\1&\text{b}&\text{ca}\\1&\text{c}&\text{ab}\end{vmatrix}$

Find the angle between the vectors with direction ratios proportional to 1, -2, 1 and 4, 3, 2.

Find the values of a so that the function
$\text{f}\text{(x)}=\begin{cases}\text{ax}+5, &\text{if}\text{ x}\leq2\\\text{x}-1, &\text{if}\text{ x}>2\end{cases}$ is continuous at x = 2.

Find the nth derivative of the following:

$y=e^{a x} \cdot \cos (b x+c)$