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All differential equations will doesn't have solutions thus it's useful to identify ahead of time if there is a solution or not. Why waste our time trying to get something that doesn't exist, if there is not a solution?
This question is generally termed as the existence question in a differential equations course
If secA= x+1/4x, prove that secA+tanA=2x or 1/2x. Ans: Sec? = x + 1/4x ⇒ Sec 2 ? =( x + 1/4x) 2 (Sec 2 ?= 1 + Tan 2 ?) Tan 2 ? = ( x +
How to find a function
Bill traveled 117 miles in 2.25 hours. What was his average speed? Use the formula d = rt (distance = rate × time). Substitute 117 miles for d. Substitute 2.25 hours for t and
Objectives : After studying this unit, you should be able to : 1. explain the processes involved in counting; 2. explain why the ability to recite number names is no in
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
Following is some more common functions that are "nice enough". Polynomials are nice enough for all x's. If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provid
Example of Linear Equations: Solve the equation 2x + 9 = 3(x + 4). Solution: Step 1. Using Axiom 2, subtract 3x and 9 from both sides of the equation. 2x + 9 = 3(
The number of integral pairs (x,y) satisfying the equation x^2=y^2+1294 is a)2 b)3 c)4 d)None of these
An ice-cream cone has a hemispherical top. If the height of the cone is 9 cm and base radius is 2.5 cm, find the volume of ice cream cone.
Two reservoirs of equal cross sectional areas (315 m 2 ) and at equal elevations are connected by a pipe of length 20 m and cross sectional area 3 m 2 . The reservoir on the left (
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