1 1 d y dy 2 3 X - х —- %D dx dx

Q: 4. § 3²*dx 5. S(e* + 1)³e*dx 6. S(e* – x°)dx

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Q: 2 dy + (1 + log y) dx d?y (1– log y ) dx2

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Q: (1+ ye + xye")dx + (xe + 2)dy = 0

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Q: 14 نقطة Q) Find dy/dx of the following * :equation (x² +x)(x' - x +1) y: dy/dx = -3/x^4 O %3D dy/dx…

A: Given y = x2+xx2-x+1x3y = x4-x3+x2+x3-x2+xx3y = x4+xx3y= x+1x2

Q: d'y |d'y -6[y"]° = 2xy 1а. 2 -5 dx d'y + 2y' –1=0 1b. 3 dx? dʻy - 3 d°y 1с. 4 = 0 .6 dx dx°

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Q: y=(6+e^x)^1/3 Find dy/dx dy/dx=

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Q: 1) ydx + xdy = 0 3) (2x+e')dx +xe'dy 0

A: In first question variable separation method is used In second question exact different ial methods…

Q: 1 6. If y = 2x + 1 d'y, what is dx? d'y d'y В. 8 4 - 6 A. dx 2 (2x + 1) С. dx D. dx dx 2 (2x + 1)…

A: NOTE: According to Bartleby's guidelines we can only do one question at a time. So i am doing Q6.…

Q: 2(y +1)e" dx + 2(e" – 2y)dy = 0 -

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Q: b) c) dx x²(x²-16)2 S S- dx 1 (4x²+3)2 S. X = X = dx = dx =

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Q: 4. x*y' = -x³y – csc(xy) 6. xy(dx – dy) = x²dy +y² dx

A: Given:- xy(dx - dy) =x2 dy +y2 dx To find:- GENERAL solution of given differential equation

Q: 10) y = e³ In x A) dy In x 3x3 In x dx dy - 4x² , dy D) dx 3x3 x³ dx +1

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Q: (x+2y) dx = dy

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Q: Solve D-E 4/xy dx + (x²+1) dy = 0

A: Given :4xy2dx+x2+1dy=0

Q: (e* + y)dx + ( 2+x+ ye )dy =0

A: See the details solution in below

Q: dy %3(x+y-1)+ dx x+y log (x+y)

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Q: х(3ху — 4у3 + 6)dx + (x3 — бх?у — 1)dy — 0

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

Q: d'y dy +9y = 6e* +7e* – log 2 6- 3x -2x dx? dx

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Q: SíS(x² + y²) dx dy 0.

A: To evaluate the given iterated integral.

Q: [[ (x + 1)" dx dy D

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Q: yln x ln y dx + dy = 0 %3D

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Q: dy 1 dx *3y = e*y+

A: The equation of the type dydx+Py=Qyn    ...i Where P and Q are functions of x only or constants is…

Q: 20. 2x (3x + y - ye) dx + (x+ 3 y + e*) dy = 0 |

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Q: 10. xy dx - (x + y') dy 0 Ans. 3 p3 +log y = C

A: given D.E isx2ydx-x3+y3dy=0---1is of the form Mdx+Ndy=0where M=x2y;N=-x3+y3∂M∂y=x2  ; ∂N∂x=-3x2

Q: 3. x dy +y dx =xg'dx

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Q: x (х+1) dw solve for dx W 2х-1

A: The Quotient rule: fg'=f'·g-g'·fg2 The product rule: f·g'=f'·g+f·g' Given: w=xx+12x-1

Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

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Q: 11. x dx dy

A: Given, ∫05∫0yxdxdyLetI=∫05∫0yxdxdyFirst integrate with respect…

Q: 1) S xe²*dx 2) S(2x + 9)e*dx 3) S xcos(4x)dx 4) Se-*sinxdx 5) Sx² Inxdx

A: Integration by parts is used when product of two functions has to be integrated as mentioned below…

Q: (x+Sy + wZ ) dzody dx dx X-つ

A: We have to find the triple integration…

Q: xy(dx – dy) = x²dy + y² dx

A: Given:- xy(dx-dy) =x2 dy +y2 dx  To find:- General solution of given differential equation

Q: 6) e2*dx +?ydy = e²*dx +ydy – 2dy + eln(x)dx

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Q: 2 TC dx = X dx exactly. 5x 7. If find e+1 +1 12

A: Given,

Q: 9. e* (y² – 4y) dx +4 dy = 0 |

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Q: (2² + a² ) dy |(x2 + a?) + 3y dx; a is constant

A: Given that, There is a non-exact and first order linear DE, (x2 + a2)dy = 2x[(x2 + a2)2 + 3y]dx,…

Q: 10/ (3e"y-2x)dx + e"dy = 0

A: We have to find the general solution of differential equation

Q: 1. r+∞ e dx x ln x - dx

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Q: (e* + y)dx + (2 + x + ye')dy = 0

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Q: (2xey + e)dx+ (x² + 1)e'dy = 0

A: We want to solve the given differential equation. To solved the differential equation, initially we…

Q: 1. S(Hx@ - 2x) dx 2.s (x" - 3X?) dx 3. S( 5xV - xo t 4x - 2) dx 4. GRND 5. dx

A: Find your answer below

Q: 1. Solve: dy e" y- = e=Y+e=2z-y dx

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Q: dy/dx=(x-7)e^(-2y) satisfy the initial condition y(7)=ln(7)

A: Use separation of variables to integrate.Given:

Q: 4) dx + xdy = x²e" dy %3D

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Q: a) Solve dy x? dx у(1+ х) b) Solve dy 4x + 3у+ 15 2x + у +7 dx

A: (a) Consider dydx=x2y(1+x2)⇒y dy=x21+x2dx⇒y dy=x2+1-11+x2dx⇒y dy=11+x2-11+x2dxIntegrating both sides…

Q: dy Find dx 5 if y = x(log2(a - 7x)) dy dx ||

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Q: (e* + y)dx + ( 2+ x + ye )dy =0

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Q: d'y y 1 dy 12 n x Solution of the D.E +- dx x dx

A: Introduction: The equation ax2y''(x)+bxy'(x)+cy(x)=0 is a Differential Equation of the Cauchy-Euler…

Q: | xy² dy dx ху

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Q: 1. ſ e3*dx dx 2. S- ex+1 dx 3. S. x/x² – 1

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Q: (у — 2) dx — (х — у —1)dy —D 0

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