Solve differential equation: 𝒙𝒅𝒚−𝒚𝒅𝒙=√(𝒙^𝟐+𝒚^𝟐 ) 𝒅𝒙;𝒈𝒊𝒗𝒆𝒏 𝒚=𝟎, 𝒘𝒉𝒆𝒏 𝒙=𝟏

Описание: Class XII Differential Equations

Q: Solve differential equation: xdy-ydx=√(x^2+y^2 ) dx;given y=0, when x=1

Previous Videos related to this chapter are mentioned in the below link:
Introduction:    • INTRODUCTION TO DIFFERENTIAL EQUATIONS  
9.7 | Q17: Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.:    • Find the equation of a curve passing throu...  
Example 14: In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?:    • In a bank, principal increases continuousl...  
Example 12: Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy=(2x^2+1)dx (x≠0).:    • Find the equation of the curve passing thr...  
9.4 | Q01: Find the general solution: dy/dx=(1-cos⁡x)/(1+cos⁡x ):    • Find the general solution: dy/dx=(1-cos⁡x)...  
9.4 | Q04: Find the general solution: sec^2⁡x tan⁡x dx+sec^2⁡y tan⁡x dy=0:    • Find the general solution: sec^2⁡x  tan⁡x ...  
9.4 | Q07: Find the general solution: y log⁡y dx-x dy=0:    • Find the general solution: y log⁡y dx-x dy=0  
9.4 | Q10: Find the general solution:
e^x tan⁡y dx+(1-e^x ) sec^2⁡y dy=0:    • Find the general solution: e^x  tan⁡y  dx+...  
9.4 | Q18: At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (– 4, –3). Find the equation of the curve given that it passes through (–2, 1):    • At any point (x, y) of a curve, the slope ...  
9.4 | Q22: In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?:    • In a culture, the bacteria count is 1,00,0...  
Ex 9.2 Q1 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y^''-y^'=0    • Verify that the given functions (explicit ...  
Ex 9.2 Q11 The number of arbitrary constants in the general solution of a differential equation of fourth order are:    • The number of arbitrary constants in the g...  
(A) 0 (B) 2 (C) 3 (D) 4
Ex 9.2 Q12 The number of arbitrary constants in the particular solution of a differential equation of third order are:    • The number of arbitrary constants in the p...  
(A) 3 (B) 2 (C) 1 (D) 0
Ex 9.2 Q7 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:    • Verify that the given functions (explicit ...  
xy =logy+C : y^'=y^2/(1-xy)(xy≠1)
Example 7 - Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx (x ≠ 0).    • Find the equation of the curve passing thr...  
Example – 9 In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself    • 12th differential eq  Example   9  
Ex – 9.3 Q4 Find the general solution: 〖sec〗^2⁡x tanydx+〖sec〗^2⁡〖y tanxdy=0〗
   • Find the general solution:  〖sec〗^2⁡x  tan...  
Ex – 9.3 Q22 In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?    • In a culture, the bacteria count is 1,00,0...  
Ex- 9.3 Q12 Find a particular solution: x(x^2-1) dy/dx=1;y=0, when x=2    • Find a particular solution: x(x^2-1)  dy/d...  
Ex 9.3 Q14 Find a particular solution: dy/dx=ytanx ;y=1, when x=0    • Find a particular solution:  dy/dx=ytanx ;...  
Ex 9.3 Q17 Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.    • Find the equation of a curve passing throu...  
Ex 9.3 Q19 The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.    • The volume of spherical balloon being infl...  
Ex – 9.3 Q21 In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
   • In a bank, principal increases continuousl...  
Ex – 9.3 Q22 In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?    • In a culture, the bacteria count is 1,00,0...  


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