5 dx (c) J 15x + 1|V25z2+ 10x

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

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Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Find the general solution of dy/dx=x-4/x^2-5x+6

A: Explanation of the answer is as follows

Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

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Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

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Q: 4.Jy2-プdy

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Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

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Q: dy 2x2+2x+1 Q 3. Examine dx for y(0.6) by RK-4 method if y(0) = 1, h = 0.2. x2+5x

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Q: Find the general solution of hp dy + 12- dx² dx 8y = 21e2x | dr3

A: To find the general solution of the given differential equation: d3ydx3−6d2ydx2+12dydx−8y=21e2x

Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: 4. S Sp(x² + y³)dxdy, wherein B = {(x, y) E R²; 0< x² + y² < 1}

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Q: dx 2. S; x²-4x+5

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Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: V16-x² .4 Evaluate: [4 16-x² J/x²+y² dz dy dx

A: We will evaluate the following Integral.

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: dy 5. S: y(1-Vy)2

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Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

A:

Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

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Q: dx xy+3x-y-3 dy xy-2x+4y-8

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Q: 1. F(x) = S t³ - 5t dt

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Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: sin(2t + ) dt JT 2 e2t-3 -3 4 e3 7 7 64e3 7 8. 5 4 4

A: Proceed as shown

Q: 4. Compute (a)음(3e2-4) dx (b) 4 dt dx-x 1+t2

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Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: -20x-2) SS f(x.y) dy dx + f(x.y) dy dx= f(x.y) dx dy, then g(6a)+h(a)= if (4)6 0

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Q: Find the general solution of 6y2 dx - x (2x3 + y) dy = 0

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Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: SSS(x² + y²) dV where E lies between x² + y² +z² = 4 and x² + y² + z² = 9

A: E

Q: d²y 10 9y = e3x + sin 3x dx2

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Q: 4. Compute (a) 4 S"(3t2 – 4)z dx - dx 'x (b) x1+t² 4 dt dx -x 1+t2 d

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Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: Vy2 -25 dy S y3

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Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

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Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

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Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: 1 dz -÷z³ = t² + 3t – 2 dt 3 z2 -

A: Differential equations and their type

Q: d*y d²y dy .3 Obtain a particular solution for dx4 + + y = x³ + 2x + 1 dx dx2

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.