Find general solution: \(y dx+(x-y^2)dy=0\)
Find the general solution: \(x\frac {dy}{dx}+2y=x^2log\ x\)
Find the general solution: \(\frac {dy}{dx}+(sec\ x)y=tan x, \ (0≤x<\frac \pi2)\)
Find the general solution: \(\frac {dy}{dx}+\frac yx=x^2\)
Find the general solution: \(\frac {dy}{dx}+3y=e^{-2x}\)
\(Find\ \frac {dy}{dx}:\)\(y=cos^{-1}(\frac {2x}{1+x^2}),\ -1<x<1\)
\(Find\ \frac {dy}{dx}:\)\(y=sin^{-1}(2x\sqrt {1-x^2},\ \frac {-1}{\sqrt 2}<x<\frac {1}{\sqrt2}\)
\(Find \ \frac {dy}{dx}:\)\(y=sec^{-1}(\frac {1}{2x^2-1}),\ 0<x< \frac {1}{\sqrt2}\)
Prove that\(\begin{vmatrix} a^2&bc &ac+c^2 \\ a^2+ab&b^2 &ac\\ ab&b^2+bc &c^2 \end{vmatrix}=4a^2b^2c^2\)
Solve the equation \(\begin{vmatrix} x+a &x &x \\ x &x+a &x \\ x&x &x+a \end{vmatrix}=0\) , a≠0
If a,b, and c are real numbers and determinant \(\Delta = \begin{vmatrix} b+c &c+a &a+b \\ c+a&a+b &b+c \\ a+b&b+c &c+a \end{vmatrix}\)Show that either a+b+c=0 or a=b=c.
Find the general solution: \((x+y)\frac {dy}{dx}=1\)
Find the general solution: \((1+x^2)dy+2xy \ dx=cot \ x\ dx\ (x≠0)\)
Prove that the determinant \(\begin{vmatrix} x &sin\theta &cos\theta \\ -sin\theta&-x &1 \\ cos\theta&1 &x \end{vmatrix}\) is independent of θ.
Compute the magnitude of the following vectors:\(\overrightarrow{a}\)=\(\hat{i}\)+\(\hat j+\hat k\);\(\overrightarrow{b}\)=2\(\hat{i}\)-7\(\hat{j}\)-3\(\hat{k}\); \(\overrightarrow{c}\)= \(\frac{1}{\sqrt 3}\hat i+\frac{1}{\sqrt 3}\hat j-\frac{1}{\sqrt 3}\hat k\)
The order of the differential equation \(2x^2\,\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\) is
The degree of the differential equation \(\bigg(\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2+\sin\bigg(\frac{dy}{dx}\bigg)+1=0\) is
Answer the following as true or false. (i)a→and -a→are collinear. (ii)Two collinear vectors are always equal in magnitude. (iii)Two vectors having same magnitude are collinear. (iv)Two collinear vectors having the same magnitude are equal.
In figure, identify the following vectors.
(i)Coinitial (ii)Equal (iii)Collinear but not equal
Classify the following as scalar and vector quantities. (i)Time period (ii)Distance (iii)Force (iv)Velocity (v)Work done
Represent graphically a displacement of 40km,30°east of north.
If A is an invertible matrix of order 2,then det(A-1) is equal to
Write Minors and Cofactors of the elements of following determinants: I. \(\begin{vmatrix}2&-4\\0&3\end{vmatrix}\)
II. \(\begin{vmatrix}a&c\\b&d\end{vmatrix}\)
Find the area of the region bounded by the parabola y=x2 and y=|x|
