(D³ + 7D² + 19D + 13)y = 0 when x = 0,y = 0,y' = 2,y" = -12 %3D %3D

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: 4x + 5 6 - Evaluate the integral dx. V3 – a? a)5 arcsin V3x + 4/3 – a2 + C b)5 arcsin V3x – 4/3 – x2…

A: =?

Q: 10.(x + Jy² + 1)dx – (y-- -(y- |dy = 0. y2+1

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Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

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Q: 3 For y = 3x + x + 3 dy = -1 = dx

A: Given that:y=3x3+x+3To find: dydxx=-1

Q: dy y3 , У (0) : 1 dx 1– 2xy2

A:

Q: ∫ 2y dx + 3x dy   where d is described by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by…

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

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Q: x² Differentiate Y = (음) %3D x²-5 dy %3D dx

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Q: 2 dx + ( 2x-y+3) dy = 0 ans. y + C = - In |2y-y+4|

A: See the details solution in below

Q: y' %3Dх (1 — у?) 2 2ху — 10у —х+5g- 0 ху +5у + 2х + 10 2х + 3 -dx + dy = у — 6

A: given differential equations are first order variable separable differential equation. We will first…

Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: 4. (x+ 2y-1)dx-(2x+y-5) dy =o

A: According to question,Given differential equation,x+2y-1dx-2x+y-5dy = 0

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

Q: S(y* - y-3)dy

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Q: 2x(y + 1) dx – ydy = 0 when x = 0, y = -2 %3D -

A: Here differential equation is given as 2xy+1dx-ydy=0or2xy+1dx=ydy⇒2xdx=ydyy+1⇒2xdx=dy-dyy+1

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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Q: 2. ( 3 x - 3 y - 2) dx - (x - y + 1) dy = 0

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Q: (3-y)dx + (y-2=) dy = 0, y(-1) = 2. ry2

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: 1- 2r (1 + y')dx - y (1 + 2x)dy =

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Q: 4. (x +y- 4) dx - ( 3x-y-4) dy = o when x=4, y=!

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Q: 6. J 4 x4-1 -dx

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Q: Find the particular Salisiles dy -2 = 5x dx + 6x1-1; y(1)= 3

A: Given : dydx = 5x-2 + 6x-1-1

Q: dy 1.3- |4 - х2 ys dx : у(1) %3D 1

A:

Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: QI Find dy for 2y2/3+xy3/20 x 0

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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: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

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Q: b) y = [ dx Integrate. 13 +5

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: ху+3x- у -3 dy %3D dx xy-2x + 4y- 8

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Q: d²y 35. Find dx2 of x² + y2 = 1 implicitly. %3D

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Q: 32. (2x-y+4) dx + (x-2y-2) dy = 0

A: Consider the differential equation(2x-y+4) dx+(x-2y-2) dy=0. The objective is to solve the…

Q: 6- 2 dx 子 メt Casy =0.

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Q: /hat is the value of dx at the point (1,0) if y = In(x² +y²)?

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Q: 2x-1 11. y = 5x+2 12. y=(5x² + 2x + 1 )3 13. y = V2x + 6 /14. y = 15. x = 2x + 3, what is dy/dx? =…

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Q: 16 dx -5y -0 dy dy 3

A: We solve this by ordinary differential equation

Q: (2x+ 3y) dx + (3x-y+5) dy

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Q: sin(3z+z²) Find y' for y = (6 – 2*)3

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Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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

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Q: 4 x dx Y 3- SSin X

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Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…