List of top Mathematics Questions on General and Particular Solutions of a Differential Equation asked in AP EAMCET

If y=aebx+cedx+xebx y = a e^{bx} + c e^{dx} + x e^{bx} is the general solution of a differential equation, where a a and c c are arbitrary constants and b b is a fixed constant, then the order of the differential equation is:
The differential equation formed by eliminating a a and b b from the equation y=ae2x+bxe2x y = ae^{2x} + bxe^{2x} is:
Number of solutions of the trigonometric equation 2tan⁡2θ−cot⁡2θ+1=0lying in the interval[0,π] 2 \tan 2\theta - \cot 2\theta + 1 = 0 \quad \text{lying in the interval} \quad [0, \pi]
If a a is a common root of x2−5x+λ=0 x^2 - 5x + \lambda = 0 and x2−8x−2λ=0 x^2 - 8x - 2\lambda = 0 (λ≠0 \lambda \neq 0 ) and β,γ \beta, \gamma are the other roots of them, then a+β+γ+λ= a + \beta + \gamma + \lambda = :
The differential equation formed by eliminating arbitrary constants A A and B B from the equation y=Acos⁡3x+Bsin⁡3x y = A \cos 3x + B \sin 3x is:
The general solution of the differential equation (xsin⁡yx)dy=(ysin⁡yx−x)dx (x \sin \frac{y}{x}) dy = (y \sin \frac{y}{x} - x) dx is:
Find the integrating factor of the differential equation sin⁡xdydx−ycos⁡x=1 \sin x \frac{dy}{dx} - y \cos x = 1 :
Determine the order and degree of the differential equation d3ydx3=[1+(dydx)2]5/2 \frac{d^3y}{dx^3} = \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{5/2} :
The acute angle between the curves x2+y2=x+yx^2 + y^2 = x + y and x2+y2=2yx^2 + y^2 = 2y is:
If p1 p_1 and p2 p_2 are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve x2/3+y2/3=a2/3 x^{2/3} + y^{2/3} = a^{2/3} respectively. If k1p12+k2p22=a2 k_1 p_1^2 + k_2 p_2^2 = a^2 , then k1+k2= k_1 + k_2 =
If y=t2+t3y = t^2 + t^3 and x=t−t4x = t - t^4, then d2ydx2\frac{d^2y}{dx^2} at t=1t = 1 is:
The equation of the circle whose diameter is the common chord of the circles x2+y2−6x−7=0x^2 + y^2 - 6x - 7 = 0 and x2+y2−10x+16=0x^2 + y^2 - 10x + 16 = 0 is:
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
If ∣fˉ∣=10 |\mathbf{\bar{f}}| = 10, ∣gˉ∣=14 |\mathbf{\bar{g}}| = 14 and ∣fˉ−gˉ∣=15 |\mathbf{\bar{f}} - \mathbf{\bar{g}}| = 15, then ∣fˉ+gˉ∣= |\mathbf{\bar{f}} + \mathbf{\bar{g}}| =
If cos⁡−1(2x)+cos⁡−1(3x)=π3 \cos^{-1}(2x) + \cos^{-1}(3x) = \frac{\pi}{3} and 4x2=ab 4x^2 = \frac{a}{b} , then a+b= a + b = :
If 540∘<A<630∘540^\circ<A<630^\circ and ∣cos⁡A∣=513|\cos A| = \frac{5}{13}, then tan⁡A2tan⁡A= \tan\frac{A}{2} \tan A =
If the roots of 1−yy+y1−y=52 \sqrt{\frac{1-y}{y}} + \sqrt{\frac{y}{1-y}} = \frac{5}{2} are α \alpha and β \beta (β>α \beta>\alpha ) and the equation (α+β)x4−25αβx2+(γ+β−α)=0 (\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0 has real roots, then a possible value of y y is:
Let [r][r] denote the largest integer not exceeding rr and the roots of the equation 3z2+6z+5+α(x2+2x+2)=0 3z^2 + 6z + 5 + \alpha(x^2 + 2x + 2) = 0 are complex numbers whenever α>L \alpha>L and α<M \alpha<M . If (L−M) (L-M) is minimum, then the greatest value of [r][r] such that Ly2+My+r<0 Ly^2 + My + r<0 for all y∈R y \in \mathbb{R} is:
If z=x+iy z = x+iy , x2+y2=1 x^2+y^2 = 1 and z1=eiθ z_1 = e^{i\theta} , then the expression z12n−1−1z12n−1+1 \frac{z_1^{2n-1} - 1}{z_1^{2^n-1} + 1} simplifies to:
Let A,B,C,D, A, B, C, D, and E E be n×n n \times n matrices, each with non-zero determinant. If ABCDE=I ABCDE = I , then C−1 C^{-1} is:
If 1−x6+1−y6=a(x3−y3),\sqrt{1-x^{6} }+ \sqrt{1-y^{6}} =a\left(x^{3} -y^{3}\right) , then y2dydx= y^{2} \frac{dy}{dx} =