Exercise 18B Archives - Noon Academy

Exercise 18B

$\text { Verify that } y=e^{-3 x} \text { is a solution of the differential equation } \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-6 y=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } y=\log \left(x+\sqrt{x^{2}+a^{2}}\right) \text { satisfies the differential equation } \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } y=\frac{c-x}{1+c x} \text { is a solution of the differential equation }\left(1+x^{2}\right) \frac{d y}{d x}+\left(1+y^{2}\right)=0 \text {. }$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } A x^{2}+B y^{2}=1 \text { is a solution of the differential equation } x\left\{y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right\}=y \frac{d y}{d x}$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } y=e^{-x}+A x+B \text { is a solution of the differential equation } e^{x}\left(\frac{d^{2} y}{d x^{2}}\right)=1$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } y=\frac{a}{x}+b \text { is a solution of the differential equation } \frac{d^{2} y}{d x^{2}}+\frac{2}{x}\left(\frac{d y}{d x}\right)=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

$\text { Verify that } y=a e^{b x} \text { is a solution of the differential equation } \frac{d^{2} y}{d x^{2}}=\frac{1}{y}\left(\frac{d y}{d x}\right)^{2}$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y=c e^{\tan ^{-1} x}$ is a solution of the differential equation $\left(1+x^{2}\right) \frac{d^{2} y}{d x^{2}}+(2 x-1) \frac{d y}{d x}={0}$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y^{2}\;=\;4a\;(x + a)$ is a solution of the differential equation $y\left\{1-\left(\frac{d y}{d x}\right)^{2}\right\}=2 x \frac{d y}{d x}$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Show that $y\; =\;e^{x} (A\;cos\;x + B\;sin\;x)$ is the solution of the differential equation $d^{2}y/dx^{2}-2\;dy/dx+2y\;=\;0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;ae^{2x}\;+\;be^{- x}$ is the general solution of the differential equation $d^{2}y/dx^{2}\;-\;dy/dx\;-\;2y=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;A\;cos\;2x\;-\;B\;sin\;2x$ is the general solution of the differential equation $d^{2}y/dx^{2}\;+\;4y\;=\;0$ .

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;e^{x} \;(A \;cos x \;+ B \;sin x)$ is the general solution of the differential equation $d^{2}y/dx^{2} \;- \;2dy/dx \;+ \;2y \;= \;0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;(a\;+\;bx)\;e^{2x}$ is the general solution of the differential equation $d^{2}y/dx^{2}\;-\;4dy/dx\;+\;4y=\;0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;e^{m\;cos^{-1}x}$ is a solution of the differential equation $(1\;-\;x^{2})d^{2}y/dx^{2}\;-x\;dy/dx\;-\;m^{2}y=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $y\;=\;e^x\;cos\;bx$ is a solution of the differential equation $d^2 y/dx^2-2\;dy/dx\;+\; 2y=0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,

Verify that $x^2\;=\;2y^2\;log \;y$ is a solution of the differential equation $(x^2\;+\;y^2)\;dy/dx-\;xy\;=\;0$

CBSE, Class 12, Differential Equations and Their Formation, Exercise 18B, Maths, RS Aggarwal

As per the given question,