Solve the following differential equation C(x)=2+0.15x,C(0)=100 - Vidyadip

Question

Solve the following differential equation
$\text{C}(\text{x})=2+0.15\text{x},\text{C}(0)=100$

✓

Answer

$\text{C}(\text{x})=2+0.15\text{x},\text{C}(0)=100$

$\text{C}'(\text{x})\text{dx}=(2+0.15\text{x})\text{dx}$

$\int\text{C}'(\text{x})\text{dx}=\int2\text{dx}+0.15\int\text{x dx}$

$\text{C}(\text{x})=2\text{x}+0.15\frac{\text{x}^2}{2}+\text{C}\ ...(1)$

Put x = 0, c(x) = 100

100 = 2(0) + 0 + c

100 = c

Put c = 100 in equation 1

$\text{c}(\text{x})=2\text{x}+(0.15)\frac{\text{x}^2}{2}+100$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A fruit grower can use two types of fertilizer in his garden, brand P and Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240kg of phosphoric acid, at least 270kg of potash and at most 310kg of chlorine.

Kg per bag
	Brand P	Brand P
Nitrogen	32	3.5
Phosphoric	1	2
Potash	3	1.5
Chlorine	1.5	2

If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?

Show that the points A(-1, 4, -3), B(3, 2, -5), C(-3, 8, -5) and D(-3, 2, 1) are coplanar.

Evaluate the following integrals:
$\int\frac{\text{x}}{\text{x}^4+2\text{x}^2+3}\text{dx}$

Examine the continuity of the function
$\text{f}\text{(x)}=\begin{cases}3\text{x}-2 &, \text{ if x} \leq 0\\\text{x}+1 &, \text{ if x} > 0\end{cases}\text{at x}=0$
Also sketch the graph of this function.

Using elementary transformations, find the inverse of the matrix
$\begin{pmatrix} 1 & 3 & -2 \\ -3 & 0 & -1\\ 2 & 1 & 0 \end{pmatrix}.$

The random variable X can take only the values 0, 1, 2, 3. Given that P(X = 0) = P(X = 1) = p and P(X = 2) = P(X = 3) such that $\sum{\text{p}}_{\text{i}}x^{2}_{\text{i}} = 2\sum\text{p}_{\text{i}}x_{\text{i}},$find the value of p.

Evaluate the following integrals:
$\int\frac{\log\big(1+\frac{1}{\text{x}}\big)}{\text{x}(1+\text{x})}\text{dx}$

Evaluate the following integrals:
$\int\frac{\text{x}^2+1}{\text{x}^4-\text{x}^2+1}\ \text{dx}$

Differentiate the following functions with respect to x:
$\text{x}^{\sin^{-1}\text{x}}$

Verify Rolle's theorem for the function f(x) = x² - 4x + 3 on [1, 3].