II. The Derivatives: Perform long method. 1. у %3D хVx — 1 2. у %3D Vx +2 t 3. x = 3-t 4. у %3D sec x 5. и 3D t2

Q: Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx²…

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Q: 2 V4-22 xy dy dx dz

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Q: 8-2² y² dzdx dy x+3y 3-3X 3-3X-y dzdyd% SS(x+y+z)dy dx dz

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Q: (16x+5y)dx+(3x+y)dy=0, (the curve pass thru the point 1,-3) (3x^2-2xy 3y^2)dx=4xydy (3X^2 - 2Y^2)…

A: Since you have posted a question with multiple questions, we answered the first one for you. If you…

Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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Q: The integrating factor (IF) of the equation: (2x³y + 4x<y + 2xy² + xy* + 2y)dx + (2y³ + 2x²y + 2x)…

A: Solution: Given: 2x3y2+4x2y+2xy2+xy4+2ydy + 2y3+2x2y+2xdy=0⋯⋯⋯⋯⋯⋯eq.1

Q: (xy + x)dx = (x²y² +x² +y² + 1)dy

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Q: 8. Find dy dx' x+2x given y = u³ + 4, u = .2

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Q: 49. Compute the derivatives, where c is a constant. (a) -ct³ (b) (5z +4cz?) (9c²y³ – 24c) dt dz dy…

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Q: 7. Given: y = 3 ; Find: dy/dt V16+tª -613 (16+t*) -2t3 (16+t*) (16+41) 글 (16+t*) ? (E) None of the…

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Q: Answer 4,5,6,7 4.What is the second derivative of  y=6x^4−3x^3+x^2−5? A.y′′=144  B.y′′=72x^2−18x+2…

A: As per guidelines we can solve only one question at a time so if you need more answers kindly repost…

Q: dx -y = 5 dt dy = 3t dt 2x -

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Q: (x² + xy – y²)dx + Gx? – 2xy) dy – 2xy)dy = 0 1 1 x3 +**y- xy? = C 1 x3 +x²y + xy² = C x²y Option 1…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if…

Q: 3t y" – 3y' – 4y = e|variationof parameters

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Q: dy = ky dx x = eky y = e-kx Option 2 O Option 4 O y = ekx x = e-ky Optio n 2

A: The given equation is dy/dx=ky.

Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: Given 5. ∫t21-t33dt6. ∫2x+3dxx2+3x-69

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

A: Topic:- differential equations

Q: 2. Find by implicit differentiation. dy dx 4 (a) x +xy +y = 5 2 2 3 =D5 3 2. (b) x- xy + y 3. =D1

A: Recall: An equation of the form f(x ,y)=0 , in which y cannot be expressed directly in terms of…

Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: Use variation of parameters method to solve x*y" – 2xy/ + 2y = x*e*. a?y" – xy' +y = 2x. y" + y =…

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Q: dx | | dt dy dt dz dt 2x + y + 2z 3.x + 6z = -4x – 3z - =

A: Given: The differential equations are  dxdt=2x+y+2zdydt=3x+6zdzdt=-4x-3z To find the general…

Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: Equation xdy + ydx = 0 y"-3y" + 3y + y = 0 (y)¹/² = √/(1+y")4 Order Degree Kind IV DV

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Q: 3y" – 6y + 6y = e" sec x (variation of parameters) -

A: The given differential equation is 3y''-6y'+6y=exsecx to find the general solution using variation…

Q: x3 +y3)dx +y2(3x+ky)dy = 0; k is constant

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: 2. S dx exte-x 3. fx sec² x dx 4. esinx cos x dx

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

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Q: 1) CSc y di + secx dy =0 CSC y Y.

A: Given query is to solve the differential equation.

Q: 5. y = gezt + cze-3t – cost o y" - 7y' +y = sint + cost o y" +y' – 6y = 5 sint – cost o y" +y' +y =…

A: Find y , y' and y'' and substitute in the given option and check which option is true. Note : As per…

Q: Find the general solution by means of separation of variables if: dy = xy -x dx

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Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: y' + 4y = e^(4t) %3D

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Q: Evaluate: J-1)–1) dy 0-my-1-등u-1)" + 즐피 ++ 11-arctan(Y )+c arctan () +c V3(2y+1) O-m-- 1³ + }n² +…

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Q: 4) = sec(x + y) dy dx 5) y' 2x-2y+1 x-y 6) y' = 2x-3y+4 x+y+2

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Q: (5v-u)du+(3v-7u)dv=0

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Q: Solve the homogenous diff equation of; dy dx x²(y² + 3) y(x³ + 1) 0

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Q: 2, x cost dt dx А. 2 В. 0 С. 1 D. x

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Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

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Q: Salve 6y"o)-5y'Lx)+Yx)= esinx+ cos2X with

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Q: - Draw the phase of:- diagram メ-Kメ=o」 No tce X dtz *- dx dt

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Q: d*y 4)5t- dt + 3t () – (sin t)y = 0 dt 4 5)(sin x)y² + 2 y = 3x³ – 5 %3D 6) xy ? + 3 xy - 2 x³ y = 7

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Q: what is the equilibrium of dy/dx = y - sqrt(y) when y >0

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Q: dx + 2x + + 6y = 2e' dt dt dx 3x +3. dt 2.+ + 8y = -1 dy dt

A: The given equation can be re- written as:

Q: Hiw 2 4t é dt 2 O Sx Sečx dx

A: (1) Consider the given integral. I=∫csc3dx The reduction formula is defined as.…

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: Solve: 3(1 + t?)(dy/dt) = 2ty(y³ - 1). %3D

A: Solve the integral 31+t2dydt=2tyy3-1. Use the separation of variable method. 1yy3-1y'…

Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: 3y" – 6y' + 6y = e sec a (variation of parameters)

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