Class 12 Mathematics - Chapter Differential Equations NCERT Solutions | \begin{align} y = xsinx:xy{'}=y +x\s
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}
y= x.sinx
Differentiating both sides of this equation with respect to x, we get:
\begin{align} y^{'} =\frac{d}{dx}\left(x.sinx\right)\end{align}
\begin{align}\Rightarrow y^{'} =sinx. \frac{d}{dx}\left(x\right)+ x. \frac{d}{dx}\left(sinx\right)\end{align}
\begin{align} \Rightarrow y^{'} =sinx + x.cosx\end{align}
Differentiating both sides of this equation with respect to x, we get:
L.H.S. =xy' = x(sinx + xcosx)
\begin{align} =x.sinx + x^2.cosx\end{align}
\begin{align} =y + x^2.\sqrt{1-sin^2x}\end{align}
\begin{align} =y + x^2.\sqrt{1-\left(\frac{y}{x}\right)^2}\end{align}
\begin{align} =y + x^2.\sqrt{\frac{x^2-y^2}{x^2}}\end{align}
\begin{align} =y + x.\sqrt{x^2-y^2}\end{align}
R.H.S.
More Questions From Class 12 Mathematics - Chapter Differential Equations
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The order of the differential equation
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is (A) 2 (B) 1 (C) 0 (D) not defined
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y = x2 + 2x + C : y' - 2x - 2 = 0
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(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
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(b) r = 4 cm - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
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(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
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