Given the first order nonlinear differential equation:dy2xdx3x + 1Choose All Correct Answers Below, and the initial condition y(1)=2, then the corresponding particular solution is:A The given differential equation is separable.3℗ y += ( ² ) √ √ (3x²+1) + 2²/7155© x ² = (²-²) √ √ (3x² + 1) + 1/72DF9y²³ = (²)√(3x²+1)1644Ⓒx²+- (²²) √ (3x² + 1) ++ ++=3None of the given answers.

Answered: Image /qna-images/answer/74532b32-159b-41d0-919c-38a7d7b9124e.jpg

Answered: Given the first order nonlinear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the solution to linear and nonlinear differential equations
Write the particular solution of the first order linear differential equation (1 + x)dy + (y - cosx)dx 0; when y(0) = 1. In writing your final answer, follow the format 2x^3ycosx-3y^2+x^3y=c. If it involved product of a variable and trigonometric function, write first the variable followed by the trigonometric function. If in a term it involved x and y, write x first followed by y whatever the exponent be. The value of the constant of integration c is written on the right side of the equation. Strictly no spaces between symbols. Do not use grouping symbols for the product or multiplication symbol. All letters should be in small letter and the order of the addends is not necessary. Use the symbol (^) caret to denote the exponent of the variable. Use the / symbol to denote quotient. =
Solve the ordinary differential equation 4x2y” + (1 - 2x)y = 0 . Then evaluate the first four terms of the solution with a rational indicial root at x = 2.9 .
13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
2 only
Find the linear homogeneous differential equation with constant coefficients and the general solution of this equation from the lowest order that accepts the solution of the expression y= 3x+2-4x²e** +e**

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